The images have been taken from the section : Relativity according to Galileo and Newton, page no.66, special relativity , A.P.French,1968 What I understood is: According to the first paragraph, Laws of transformation are needed so that a theory which describes a phenomenon w.r.t. one reference frame could be applied to explain the same phenomenon w.r.t. another reference frame. Does it mean that Laws of transformations are different for different theories? A physical statement of what these invariants are is called a principle of relativity. For Galilean transformation, acceleration is invariant. So, does it mean that the following statement: "Acceleration is invariant under Galilean transformation ." is a principle of relativity for Newtonian dynamics. So, for different theories , there will be different principle of relativities. Right? Fundamental equations of theory usually defines the principle of relativity applicable to the theory. e.g. The equation F = ma defines the principle of relativity, i.e. force in Newtonian Dynamics.